Environments use sinusoidal function to model populations of predators and prey in the environment. In particular study, the population of rabbits was modeled by the function. R(x)-1500 sin (pi/2(x+pi/2))+2500 The population of wolves in the same environmental area was modeled by the function.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: